Problem: Multiply the following complex numbers: $({1+2i}) \cdot ({1})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1+2i}) \cdot ({1}) = $ $ ({1} \cdot {1}) + ({1} \cdot {0}i) + ({2}i \cdot {1}) + ({2}i \cdot {0}i) $ Then simplify the terms: $ (1) + (0i) + (2i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 1 + (0 + 2)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 1 + (0 + 2)i - 0 $ The result is simplified: $ (1 - 0) + (2i) = 1+2i $